Today in inquiry, our goal was to discuss what didn’t make sense. And in discussing what didn’t make sense, we made a lot of progress towards making sense of things. Here are a few quotes from today’s daily sheets.

“Another thing that didn’t make sense is why there is an image at all. This isn’t even a question I had before–I never even really considered it.”

“I understand ____’s idea about _____, but I am not quite convinced that this is correct.”

“I do not understand how all of the “required rays” to make the picture end up going through the hole. It seems too ‘lucky’.”

“I do not understand how the whole image gets through… where are the boundaries? Is it here? here? Somewhere rays from the very top can’t make it down? Where does that happen?”

“Everything made sense, but also, none of the ideas we discussed are thought through enough, at least not in my head, to decide which is right.”

“I know that a bigger hole makes it blurry, but I’m questioning why it wouldn’t be more clear with more light getting through with more colored rays”

“It was the questions we asked today that made it finally start to come together. ”

There are several reasons why talking about what doesn’t make sense works: It invites people into the conversation that might not contribute otherwise. It sets a tone of discourse around uncertainty, problematizing, and genuine understanding.

But I think, a strong factor is this one. Once people voice their concerns about what doesn’t make sense, those concerns can then function as criteria for evaluating the strength of any proposed explanation. When someone says they have an idea, we can all judge the quality of the explanation in terms of whether or not it addresses the concerns, questions, and issues that have been raised. This, in turn, is what makes our collective activity scientific.

 

This year in algebra-based physics, I switched to larger-grain standards that emphasize synthesis; where  as previously had finer-grained standards and fine-tuned assessments that target only one specific skill at a time. You have to remember that my standards based assessments system (with learning goals and reassessments) happen before a common, high-stakes exam.

Typically, on the first exam, the distribution of grades from my section would have looked like this

4 As

14 Bs

10 Cs

4 Ds

This semester my grades look like this

10 As

9 Bs

4 Cs

4 Ds

5 Fs

The average score remained about the same, but the distribution changed a lot. I think I can speculate about why, but I don’t like what I have to say. Sure, it could be random noise, but I sort of predicted this might happen based on informational observations. That is, it could still be random noise, but I’m subject to confirmation bias. Anyway, here’s my tentative explanation:

With the fine-grained standards, struggling students would get repeated practice on basic skills (e.g., distance vs position vs displacement). Non-struggling students would get it right on the first shot, and not need to reassess. This system made sure that struggling students had mastered very basic skills before the exam, but perhaps left the non-struggling students with less opportunity to practice honing their problem-solving skills. Because of this, my old distribution had a high floor, and relatively sparse ceiling.

This semester, with the synthesis-level assessments, we get a different picture. Struggling students make lots of mistakes on the more difficult assessments; and without targeted, focused goals to practice for reassessment, they don’t develop sufficient basic skills they did in the old system. They may just get swamped in trying to figure out how to solve complex problems. Non-struggling students don’t get it right the first time, but they get close enough to learn something, and take up opportunities in reassessments to hone their skills. Because of this, the ceiling gets more populated, but the floor drops down.

So is my assessment system now just helping students who would have done good do great? Was my old system better at helping struggling students? I can’t be sure, but I’m thinking.

Here it is. The three questions I always ask the day after the exam, before they know how they did. So readers, what do you notice? What stands out to you? What seems common? What’s seem unique?

What happens in class that is helpful for your learning? What specifically is helpful about it?

I really enjoy the group work on the whiteboard. It helps to see all the work and hear how people process information.

Repeated and varied demonstrations help me to learn the concepts. Repetition is a strong learning tool of it’s own,  but additional demonstrations tie the math to the actual results.

We do a lot of practice problems, which I like. I think learning goal quizzes do really help me. I also think that working in groups and discussing how we figure something out together is also helpful. I like the whiteboards.

Showing and experimenting on the information. It allows me to comprehend from various scenarios.

We do a lot of discussion and hands-on. Lectures are made as simple as possible to explain. Group work is helpful, especially the whiteboards.

I love the problems we get to do. I like watching a problem working out and then completing it with my group.

Demonstration and diagrams on the board are both helpful in understanding concepts.

The explanation of why as opposed to just equations is helpful.

Hands-on experiments are great. Working out problems on whiteboards.

The constant examples problems and group work. It gives us variation in what we do and what we might see on the exams.

At 1st I hated quizzes and reassessments but they really are helpful, because they make us study, and help us get ready.

Practicing problems on our own.

Hands-on activities, where I can witness what we are trying to measure and understand.

I was skeptical of reassessments since they seem to just add more quizzes to the ones we’ve already have, but now that the test is over, I’ll say I was very confident going into and coming out of the exam. I think that had a lot to do with it. The group whiteboard activities are also helpful when we first introduce ideas, too.

Working in groups, because it helps me to learn by playing ideas off others.

You explaining things combined with exercises. We get a lot of practice working problems in class.

The thing that’s most helpful, and also the most annoying, is assessments. I learn so much more by being forced to do homework problems and retake quizzes until I’ve mastered it. And honestly, I wouldn’t do as many hw problems if it weren’t for it.

Example problems, hands-on stuff help make the information relatable.

Practicing problems in group-building a better understanding of physics.

Hands on physics, see what happens. I don’t like being just told. Seeing is worth more.

White-boarding activities are helpful. We collaborate as a group to solve it.

Working problems with actual examples. It helps because you can relate it to real examples, show how things work instead of just believing without proof.

Working in groups, bantering back and forth, these held to solidify ideas in my mind. Working problems as  group helps learning problem solving processes.

Working through different examples is good.

What happens in class that is not helpful for your learning? What

Group work. This is a problem specific to me–lack of people skills and social anxiety.

Nothing is unhelpful, but some activities are not as helpful as others, but I cannot think of any that are just not helpful.

A change that may be beneficial is a review day for upcoming tests.

I always like to see everything worked out, so when steps are skipped sometimes it’s not helpful and I get lost.

The lab calculations because I am usually confused about exactly what to do, because lab manual and what we need aren’t always the same.

A class period workload is unhelpful in that those who work at a faster pace, the down time waiting for the rest of the class brings boredom sometimes.

Hearing people explain why they think an incorrect answer is correct usually just confuses me.

I think the clicker questions aren’t hard enough. I would like to see them involve more challenging questions or problem.

My group doesn’t really discuss all that much.

Sometimes class can get tedious. Solving more equations in class would help retain that knowledge more.

They learning quizzes are not helpful, just stressful.

Sometimes there are long gaps that seem to appear when one group finishes and has to wait on other groups to finish up.

Not a big fan of in class experiments. Seem to take a lot of time. I understand that some people are able to better grasp things that way.

The boards and class discussion help a lot, hearing ideas and helping each other out.

Class is just too long. And sometimes we have to wait for other groups to finish.

Anything Else you Want to Tell me?

I honestly hate reassessment quizzes But! I get why we do them.

I need to come to office hours more. The one time I came it was very helpful.

The reading quizzes online aren’t a huge help to me. They do make me skim the reading more than usual, but I get more from class.

Reading quizzes, because I often don’t understand the reading before class.

I wish we would go over 3+ problems together that we would likely see on the exams more often! Give more examples and break them down more.

I’m not sure that I can get the formulas but I know some people who do. I would like more “this is why” because I’m having a hard time executing.

I’m going to have to work harder, a lot harder. I’ll have to become better with my time management even with everything that’s going on.

 

What Brian is thinking:

• Online Quizzes: I may be willing to drop or revise my online pre-class quizzes. I’m actually thinking of changing it to just, “Tell me about one thing you learned from the reading that makes sense to you.” “Tell me about some of the ideas from the reading that you have questions about or feel confused about. Be as specific as possible.”
• Finishing Early / Down Time: I want to chat with students about things they can do when they finish before other groups. They have group projects starting up, so they can use that time to chat about that. I could also do a better of job of monitoring time, and having extension questions ready.
• Step-by-Step: In emphasizing reasoning and concepts, I do sometimes de-emphasize some aspect of procedures for tackling problems. I’m better at this than I was, but I still have room for improvement.
• Lab Write-ups: I need to better communicate lab write-up procedures, align what I say with our new lab book (things have changed this semester, and I’m sometimes communicating things accidentally based on old expectations), and I also need to work to minimize the amount of bullshit that’s required from the lab white still emphasizing the key skills they do need.

In our third week of “Step 1: Inquiry Approaches to Teaching”, we were given the details of the lesson we’ll be teaching in a few weeks time.  All lessons plans follow the 5E model (engage, explore, explain, elaborate, evaluate). All of the E’s in the lessons are filled out more or less except for the “Engage”. In addition to figuring out what we’ll have to do for the engage, we are asked to write up a few sentences about the concepts that are the focus of the lesson, identify the common core standards that apply to the lesson, and to write three learning objectives based on the concepts and standards.

For example, the lesson I’ve been assigned (for fifth grade) involves an activity in which students are given a collection of different length measuring instruments–yard sticks, string, a surveyor’s wheel, measuring tape, etc. Students are supposed to plan how they might determine the perimeter of their classroom, in the context of how we’ll be replacing all the baseboards. The ultimate goal is to determine the price of replacing the baseboards. That’s really just the explore of the lesson. It’s not really clear from the lesson plan we’ve been given what they intend to happen with the explain, but it seems as if maybe students will be sharing their results, explaining how they arrived at them, and the teacher helping the class reach a consensus and introduce terms like perimeter.

One of the issues that has come up is that the menu of lessons teachers can pick from for us to teach were aligned to the old TN state standards, and so now the menu of lessons don’t quite match the way they should. It’s not too much of a problem, but it means re-thinking what the learning objectives for lesson might be. For example, ideas about perimeter used to be a grade 5 standard in the old TN standards. So previously you could find standards about perimeter on the grade level. Now, with the common core, perimeter is a grade 3 standard.  They didn’t want me identifying grade 3 standards for a fifth grade lesson, so we had to go shopping for possible grade 5 standards. One of the standards in grade 5 that we found is something like “solving multi-step, real world problems that involve unit conversions with a measurement system”.  So, now we’ve made the perimeter lesson just the context for a learning objectives about problem-solving and unit conversions.

In that context, my quick draft for learning objectives were the following:

• SWBAT communicate plans about how to measure the perimeter of an irregular shaped polygon (including which tools they’ll use, how they’ll use them, and why their plan will yield the perimeter)
• SWBAT identify situations (or aspects of a problem) where unit conversions might be necessary and explain why.
• SWBAT to correctly perform unit conversions where whole numbers are involved.

I was in the classroom yesterday making observations and students have been practicing unit conversions, so it seems like a reasonable thing to ask them to do in the context.

Forward Rather than Backward Design

One of the things I’ve been thinking about in this process is what early teaching practices students are being introduced to either explicitly and implicitly. One of things we seem to be doing is saying, “Hey here’s this good/cool lesson. Now go figure out what standards might be there”. I’ve been thinking about this in the context of Wiggins’ Backwards Design, and how we are doing the exact opposite of this. I’m not saying that this is good or bad at the moment, I’m just noting it. I heard that they started teaching this course with students designing lessons, but it was just too much. So they switched to giving students lessons to go with, giving them an opportunity to flesh them out, practice them, and link to standards and learning objectives.

Next week, I have to have my lesson all ready to go for a practice teach, so I’ll try to post more about how that gets fleshed out.

 

 

One thing I’ve been trying to do in intro physics this year is get students working on problems that are more challenging that what they’ll see on the exam. Typically our first exam  has a back-and-forth problem where each stage is constant velocity, an acceleration problem that has no back-and-forth aspect, and a free-fall problem where there is a turn-around point.

In my class, we’ve been doing more horizontal acceleration problems that include turn-around points (e.g., using fan carts along a track). This gives students more practice thinking about direction of velocity and acceleration, instead of just memorizing that for free-fall that acceleration is down.

We’ve also been doing more multi-stage problems where parts of it are constant acceleration and others parts of it are constant velocity (e.g., a car speeds up, maintains a speed, and then slows down). This gets students practicing identifying when they need to apply a constant acceleration model or constant velocity model, and also thinking about how to string them together (e.g., the final velocity in stage one is the constant velocity in stage two).

We’ve also been doing more problems involving multiple moving objects (e.g., where or when will two objects meet?). These problems are really the only problems that get students distinguishing among position, distance, and displacement in my mind.

One of the things I like about this is that it means students will be evaluated at level below where I’ve been helping them get to.  However, it has had some interesting negative consequences for exam preparation. Before, students just had to memorize three kinds of problems–back-and-forth, 1D acceleration, and free-fall. They could get by just memorizing, “On these kinds of problems you do this, and one those kinds of problems you do that.” For example, students would know to use multiple stages only on the back-and-forth problem, not on 1D acceleration or free-fall, where they should just set up their variables and plug into one of the equations. Since I’ve been having them practice lots of mixed problems, where there are multiple stages of constant velocity and constant acceleration, students can’t rely on just memorizing. They actually have to make sense of the problem and thinking about what to do.

In this context, I’ve seen students struggling or making “mistakes” I’ve not seen before.

For example, a problem will say, “A fan cart is given a quick push to right, such that it starts with an speed of 12 cm/s. The fan is oriented such that the cart immediately starts slowing down. Three seconds later, it’s moving to the left with a speed of 3 cm/s.”

I’ve seen more students trying to figure out the kinematics of how it go up to 12 cm/s, or thinking that it maintained that 12 cm/s for some amount of time. Or, because the problem doesn’t explicitly use the word acceleration (it’s inferred based on the context and the fact that we’ve been observing fan carts in class a lot), some try to treat it as a back-and-forth problem where it had a constant velocity of 12 cm/s for a while, and then a constant velocity of 3 cm/s for a while. It certainly could be I’m writing ambiguous questions. The thinking and struggling they are doing is fine, and it’s productive for them to be struggling with this. But I fear this may hurt them on the exam–instead of just launching into a quick procedure, based on “which of three possible problems is this”, they’re going to be actually thinking on the exam. It’s not necessarily true that you do better on tests when you do more actual thinking. Tests often favor over-practiced routines. I think I’ve been preparing students to be more adaptive, at the expense of having over-practiced a small number of routines.

While I do want my students to learn meaningfully, I also want them to feel like they’ve been well prepared for the exams, especially the first one. It gives them confidence, and leads them to trust me and what we’ve been doing in class to learn even more. Maybe all my concerns are overblown, but I guess we’ll have to see.

 

 

In addition to writing about [Back to School], my experience being a student again pursuing a minor in secondary education, I’m also hoping to write about mistakes I make during inquiry teaching. Mostly by mistake, I mean not supporting students in their own inquiry. Here’s my mistake of this week.

Using My Authority To Undermine My own Goals

One group is getting really interested in how projectors work, seeing it as possibly analogous to how our box theatres work. They did some tinkering around with our overhead projector, noticing that the lens also flips the image. They explored with and without the mirror, and tried other investigations to see if they could get images to flip using mirrors. Being kind of stuck or just interested in what the different parts of the project might be they started looking some information online. When I came by, I noticed they had some diagrams on their iphones. Instead of engaging them with what they were doing, asking them to tell me about the diagram, what they were thinking, or what they were hoping to learn from the diagram, I sort of came over and “shot down” getting on the internet. My secret concern was that using the internet would lead them to use such information authoritatively in an unproductive way. I just assumed that they would use it unproductively, instead of engaging with them and trying to help them engage with it productively. I even could have, after engaging them, voiced my concern in a friendly way, while still letting them know that I trust them as adults to make decisions about how to research and pursue their topic. Instead, I actually created the situation I was worried about–I came over as an authority and told them “not to get answers from the internet”. Ugh! The biggest problem is I as a teacher don’t know what they are thinking and doing, because I failed to do any meaningful proximal formative assessment.

What I really appreciated was that one of students from the group wrote on her “Daily Sheet” that she was concerned that I was stepping in too early with their group, not giving them time and space to do their thing. I feel bad about the mistake I’ve made, but glad that this student felt comfortable sharing their concern with me.

Anyway, what do you think about mistake? What mistakes have you made this week?

Two of the classes I teach for our pre-service physics teachers are 1-credit content workshops called “Physics Licensure I & II”, which students take after completing introductory physics. Some in their sophomore year and some in their junior year. Initially there was just one course, and it was intended to sort of be a review to help students prepare for the Physics Praxis. Now we have two courses and there is less focus on Praxis Prep.

The first courses covers kinematics, forces, momentum, energy, and rotational dynamics. The second courses covers electricity and magnetism. I’d like to have room for optics / waves and thermodynamics, but that’s not happening at the moment.

Course Goals

• To deepen conceptual understanding and reasoning in introductory physics
• To provide exposure and familiarity with research-based curricular materials
• To begin developing some knowledge of student difficulties and to engage in practices of interpreting student thinking.
• To strengthen and broaden problems-solving approaches
• To introduce students to structure of AP physics courses and AP exam problems
• To develop an awareness of what productive group work feels like and to become aware of and practice specific talk moves that can support productive group work.
• To practice articulating one’s reasoning “on the fly” and practice listening in order to make sense of other learner’s attempts to express their reasoning.
• To practice writing up solutions to physics problems in an organized and clear manner that mirrors the needs of professional teaching.

These goals are important for lots of reasons, but here are two specific things about our situation that makes these courses and goals especially relevant.

(1) Although our introductory physics courses have many reform-elements in place, there is still insufficient opportunity to develop conceptual understanding. There is too much emphasis on plug-and-chug approaches to solving problems, and our labs emphasize verification too much. As such, students leave their introductory physics courses very underprepared in terms of conceptual understanding, even if they got A’s.

(2) Many of our physics majors, and almost all of our pre-service teachers, go through the algebra-based physics course. The problems isn’t that it’s algebra vs. calculus. Rather, it’s more about the difficulty and rigor of the kinds of problems that students have to solve. In the algebra-based courses, there aren’t enough challenging problems where students have to draw from multiple different big ideas in physics–use energy, momentum, and projectile motion for example. Or enough force problems where students have to contend with multiple algebraic equations coming from multiple interacting objects. Most of our students would not be able to pass the AP exam coming out of our introductory sequence, but it’s a course they are likely to teach.

Course Structure

The course has been structured so that anyone in the department should be able to teach it. For now, I’m teaching it, but I want it to be a course that can easily be taken over. This is how we are currently working toward supporting the course goals while also making it possible to handoff the course in the future.

(1) Students work through Tutorials in Introductory Physics curricular materials. Students do all the pieces–taking online pretests before class, work through the tutorial in groups during class, and do weekly tutorial homework. Right now, this is the main part of the course, and is what really makes the course “handoff-able”.

(2) Students have readings about the Praxis Test and the AP Physics Course. Right now I’m doing a lot with this beyond assigning the readings. We don’t have a lot of time in class to discuss, and I’m already assigning a fair amount of homework. But I’d like to have some part of the class in the future be about summarizing / consolidating someof the stuff from the reading.

(3) Students are assigned AP physics exams problems, and must turn in solutions that meet specific criteria for professionalism.

(4) On days where we don’t use all 90 minutes to go through the in-class tutorial, we end the day by examining and discussing example student responses to the pretest they took. I think I’d like to push the class time to 120 minutes, so we always have time for this, but it is only 1 credit class. I’m grateful to the folks at the University of Washington (particularly Peter Shaffer) for providing these example student work and getting my set up with the online pretests. I have been really amazed at the Office tool called “Mail Merger”, which they showed me. I think it was originally intended to take a “participant list” and write template letters that were addressed to each participant. But you can also use it to take “student responses” from an online quiz that are in an excel spreadsheet and re-embed the responses in a template that looks like how the online test looked. This way you don’t have to store “100 student responses” in word files, you store 1 template in word and an excel spreadsheet. When you are ready, you can have mail merger put them together, and have a bunch of different student responses to hand out.

(5) During the tutorial time in class, I try to do a lot of scaffolding, modeling, and giving feedback on group work. I even give very specific talk moves I want them to practice like. For example, I have them practice when somebody gives an answer that you agree with to not just say “Right,” but to say “I agree…” and give a reason why you think so as well. I also have them practice noticing when and if someone hasn’t said anything a while and to ask, “So-and-so, what do you think about this question?” So far, I’ve been doing this on the fly in an opportunistic fashion. I do it deliberately, but I should think more carefully about how to make sure this goal is being met. This, at the moment, is the least hand-off-able.

Other tidbits:

Right now I have two pre-service teachers returning as “undergraduate teaching assistants”. The day before class, we go through the tutorial to prepare for class, but we also go over students’ pretests responses. They help facilitate group work, and I think this is a real valuable experience for them.

A lot of the grade is based on participation–doing the pretests and being engaged in the tutorial. But both the tutorial homework and AP homework is graded for correctness. There is also a final that will consist of some tutorial-like problems and an AP-style problem. The final is only worth a little bit, enough to make it difficult to get an A from just participation and homework alone.

The first semester course (Physics Licensure I) is now a pre-requisite for taking “The Teaching of Physics”, which is more about pedagogy. This will guarantee a minimum of conceptual understanding, exposure to research based materials, and the beginning of knowledge and practices of interpreting student thinking. I’ve decided, however, that non-teaching physics majors with a late interest in teaching can take the teaching of physics course, but only if they can perform well on the FMCE and take Physics Licensure II as a co-requisite.

Changes for Next Time:

* I want students to write up after the tutorial something about what the learning goals for the tutorial / what they learned.

* I want students to go back and revisit their own pretests after completing the tutorial and looking over and discussing student mistakes. They will have to not only make corrections, but explain what was wrong with their thinking and what they know now that will help them not make that mistake in the future.

* I want to have an activity where we look at example teacher solutions to problem and collaboratively come up with a rubric for assessing the quality of their own solutions.

Thoughts, feelings, suggestions, questions, concerns? I’d love to hear about it.

I’m certainly not an NGSS hater. I actually find much to like about it, even if there are specific things I don’t like. In this post, however, I want to talk about one potential flaw I see in how the NGSS conceptualizes progress in scientific practices.

The trap I think the NGSS seems to fall into is seeing growth of sophistication in practices as based on age, rather than based on depth of knowledge and experience in a particular domain. This is a common “trap” to fall into–thinking that sophistication in reasoning or skills unfolds with age rather than unfolds with the depth of knowledge and experience someone has about a particular topic. Lot’s of people have written about this–one in particular that I think is great is Metz’s 1995 article called, “Reassessment of developmental constraints on children’s science instruction.” From what I know, a lot of the “stage-based” development stuff has roots in particular (arguably flawed) interpretations of Piaget’s work, and a lot of subsequent work to debunk such interpretations are based on findings that even young children can engage in sophisticated reasoning when its about things they have lots of knowledge and experience about.

Let’s start with the eight NGSS science and engineering practices:

1. Asking questions (for science) and defining problems (for engineering)
2. Developing and using models
3. Planning and carrying out investigations
4. Analyzing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations (for science) and designing solutions (for engineering)
7. Engaging in argument from evidence
8. Obtaining, evaluating, and communicating information

On the one hand, the NGSS is very deliberate in saying that children should be expected to engage in all practices in all grade bands. And NGSS is very explicit that what develops over time is the sophistication of practices, not which practices students engage in.  We can see this emphasis in the guidelines they provide about the practices:

Students in grades K-12 should engage in all eight practices over each grade band. All eight practices are accessible at some level to young children; students’ abilities to use the practices grow over time…

Practices grow in complexity and sophistication across the grades. The Framework suggests how students’ capabilities to use each of the practices should progress as they mature and engage in science learning…

So now let’s focus on one practice and how it unfolds in sophistication–asking questions. I want to argue that the particular articulation of sophistication falls into the trap they seem to want to avoid. Now, keep in mind, there’s a lot written down about questioning in the document, and here I just take a particular slice of what NGSS has to say about the development of questioning practices over different grade bands. So here’s a slice:

K-2

Ask questions based on observations to find more information

3-5

Ask questions about what would happen if a variable is changed

6-8

Ask questions to clarify and/or refine a model or an explanation

9-12

Ask questions that arise from examining models or a theory

In this slice of the progression, students might be understood to change over the years from asking questions based on observations to asking questions based on models and theories. That is to say, it seems as if, in K-2 students should be expected to ask questions about observations, but they should not be expected to ask questions a kin to, “I wonder what would happen if we changed this?” Grade 3-5 students can ask “What if” questions, but shouldn’t be expected to have questions based on ideas they either have or have heard about how something works.  Middle school students can be expected to ask questions about a model or explanation, but they shouldn’t be expected to ask questions that involve comparing and contrasting different ideas.

Maybe this doesn’t sound crazy to you, but it kind of sounds crazy to me. Why it sounds crazy to me is because I think in almost any inquiry you do with anyone at any age is likely to follow that progression, give or take. Students will likely initially be thinking about something they’ve seen. And their questions will flow from that. As they get to tinker with the phenomena, they are likely to wonder about what might happen differently if different features of the scenario were changed. As they start to develop ideas about the phenomena, new questions stemming from their ideas should arise. Finally, as students think and share about the different ideas they have, new questions should arise based on differences between those ideas. That progression doesn’t take 12 years. A few hours, a few days, a few weeks, depending on circumstances, the content, and the students. But not years.

My contention is that if you give me some college-age kids, our questioning practices won’t start off in the 9-12 band. They will almost necessarily start at the K-2 / 3-5 band, if it’s an area these college students don’t know a lot about. Of course, over time, our questions will progress in sophistication. My other contention is that if you give me some kindergarteners, the same thing will happen. Kindergarteners aren’t stuck asking questions on the low-end. As they get to explore, think, talk, and share, their questions should stem increasingly from the ideas they have. Now what might be true is that it might take different age students differing amounts of time to get from one end of the progression to the other, but I’m even hesitant to commit to that.

Here’s an example. This semester in my inquiry class, we are investigating light and color as usual, beginning with observations of images through pinholes. Our initial questions were things stemming from observations and questions about changing variables.

“Why is the image upside down?” (an observation)

“I wonder what would happen if we used colored paper instead of white paper?”

“Would we see a panoramic view if we poked holes on multiples sides?”

“I wonder if it would still work inside rather than outside?”

“I wonder what would happen if we used a different kind of tape?”

For our first two homework assignments, students have been articulating initial ideas about how it might work. By articulating ideas and sharing ideas, we have new kinds of questions.

“If we poke the hole toward the bottom of the box, will the image now be right side up?” This question is a what if question, but stemming from an idea that it was the location of the hole toward the top of that mattered and the particular angle light had to enter the box.

“Is the image flipping outside of the box or inside the box?” –> This question comes from comparing two different models, one showing an image flipping when light from sun bounces off a flower, another model showing the image flipping as light bounces of the top and bottom walls of the box.

“Does light bounce off objects in all directions or shoot in one straight line?” –> This questions comes from comparing different diagrams that were made, some showing light bouncing one way and one showing light bouncing another way.

It didn’t take us long to progress from one end to other, but that didn’t happen because these students are adults. It happened because (1) students were given something interesting to observe, (2) they were given time, space, and resources to explore and tinker, (3) they were asked to articulate their ideas, and (4) we spent time explicitly sharing ideas in order to compare and contrast our different ideas. That said, were not done–as we cycle through different observations and ideas over weeks, we’ll continue to ask questions all over the progression.

Anyone who has taught even young children knows they are capable of asking what if questions, and capable of hearing others ideas and responding with questions.

One argument someone might make against my issue is this. The NGSS doesn’t say that students shouldn’t engage in all questioning levels all the time, because NGSS does not describe curriculum or pedagogy. It is only saying what students will be expected to do. So, Brian is free to engage his kids in questioning at all levels, but we will only test them on questioning at the low end. I say that’s fine, but then I don’t the logic of why the progress is how it is.

What do you think? Am I crazy? Does this matter or no?

Two Days of Step One: Inquiry Approaches to Teaching

The first day, we basically went over the syllabus, filled out scheduling information, and got the tour of the MTeach office, supply closest, and staff. Our first homework assignment was to read a brief paper about characteristics of effective teachers and reflect on a previous teacher that was memorable to us. The message of the paper was fine (care about your students, create a sense of belonging, be fair, be willing to admit mistakes, have high expectations, etc) , but it purported to be research-based and was really just a list of things that pre-service teachers wrote on a survey about what they liked about their most memorable teacher. It’s kind of like determining what makes effective doctors by asking Premeds what they liked about their doctor. All and all I think it was a good first assignment, but in writing it I was reminded how difficult it is to write school assignments, especially when there is neither an authentic audience to read it nor are you in a position to be writing for yourself. Nonetheless, I used the prompt to start a good discussion with my wife, which was meaningful and useful to me. That’s going to me my goal with homework–for it to provoke meaningful discussion, even when I work hard to find a kernel of provocation.

On the second day, we were given our teaching assignments. I’ll be observing the same 5th grade class on two Fridays in September and then teaching three lessons to that same class throughout the semester. Unlike most students who go through program, I won’t have a teaching partner. Over the weekend I’ll be meeting with my mentor teacher, and I’ll find out what lessons I’ll be asked to teach. My understanding is there is a menu of lessons that teachers can pick from.  You aren’t expected to do any lesson planning. Rather you are expected to carryout a pre-planned lesson.

On the second day of the class, we also experienced a model lesson and were introduced to the 5E lesson plan structure that is used in the program. The 5E’s stand for Engage, Explore, Explain, Elaborate, and Evaluate. The model lesson involved 2-digit multiplication. I’ll say more about the lesson later.

At the end of the lesson we got a brief introduction to learning objectives and standards. Tennessee, like many states, is in the middle of transitioning from our old state standards to the Common Core Standards. We had a chance to briefly glance at some standards related to the lesson, ultimately finding that it was easy to find Tennessee standards that fit the lessons, but difficult to find any Common Core Standards. Mostly this was because the lesson involved doing multiplication, and little interpreting, problem-solving, explaining, etc.  We were also briefly introduced to the ideas about how objectives should use “action” verbs and should be measurable, trying to avoid vague words like “students will understand that..” or “students will know that…”  I’d be interested to know more about what students walked away from this tidbit on learning objectives, because I feel like this all happened really fast and students don’t have a lot of context and background knowledge related to this.

The Model Lesson–Maximize Your Product

Anyway, so the lesson involved using ideas about place-value to maximize products. There was a brief “engage” at the beginning of the lesson that involved some story about buying candy. The story was basically about if you should choose to go to store that had 42 bags each containing 59 lollipops or 94 bags containing 25 each.  Could you figure out which would get more lollipops without formally doing the multiplication? Then our “explore” was the following game. In pairs, you would take turns rolling a die. You had a four boxes on a piece of paper representing a two-digit multiplication problem and you had to decide where you wanted to place the number that was rolled so that at the end of four rolls, your product would be as big as possible. You did this a couple of times. The “explain” part of the lessons involved students coming up to the document camera to explain the decisions they made and to work out the two-digit multiplication, and the teacher emphasizing ideas about place value. We didn’t do the “elaborate”, but it was mentioned that normally students would go back to play game again this time trying to minimize their products. There was also some evaluation questions, which were mostly just worksheet problems that we also didn’t do. The lesson ended with returning to “engage”, where at least one interesting mathematical idea came up, but mostly it just involved having us do the multiplication that was in the candy story.

Some positives I see in this model lesson:

Students were engaged in a task that required some mathematical decision making, rather than just procedural steps alone.

Some students were asked to explain their thinking and reasoning in context of the work they did, and other students were expected to listen. It’s nice to emphasize that the explain part of the lesson involves students explaining, not just the teacher.

The teacher did little lecturing. Rather, the teacher help consolidate and synthesize some ideas in the context of students’ just having shared their work.

Things I thought about during and after the lesson

#1 Engaging Ideas?

Being in the room, I didn’t have the sense that students’ mathematical ideas were really engaged in the lesson. For context, I’ve seen how our pre-service teachers often seem to have about odd ideas about the “engage” part of the 5E model, almost as if it meant “be entertaining”. In my mind, while an “engage” can certainly be entertaining, the point of the engage is to engage ideas, so as to possibly cultivate a sense of curiosity, wonder, puzzlement, surprise, or purpose. With this lesson, I could easily see students walking away from the lesson thinking, “Kids like Candy. This was a good engage because it was about candy. Candy engages kids.”  What could have made this engaging of our ideas is if we had the opportunity to think about which one we thought was more candy, to articulate our reasoning and hear others’ reasoning, and then commit to an answer. This would also be an opportunity to model good classroom discourse.

#2 Learning Goals?

The discussion of learning goals centered around two-digit multiplication, and there was sort of a message being sent that this lesson was good because it got students practicing two-digit multiplication without it being a worksheet. Almost like it was good because it a fun exercise that tricked students into practicing math. I’m not saying that’s bad, but I was wondering whether the goal of the lesson was more about estimation and place value, and how we can use place value to estimate. One of the reasons I thought this is because everyone proceeded to do all the multiplication using the standard algorithm. [ I used partial products mostly, for example solving 41*41… by saying 41*10 = 410 takes care of 10 of the 41s, then adding 410 four times to get to 40 “41s”, and then adding one more 41 to finish it off. ] The reason I don’t think this lessons was much about two-digit multiplication is because it wasn’t really about ways of thinking about or doing two-digit multiplication, it was just the procedure used to check to see who had maximized their product. The lesson sort of has to assume you already know how to do it. And now maybe it’s getting you more chance to practice it or a chance for the teacher to assess students’ proficiency , but the mathematical thinking would seem to still be mostly about place value and using place value ideas in the context of the meaning of multiplication. Of course, lessons can have layers of learning, and I’m not saying that you couldn’t have multiple goals, or different goals for different learners.

Thinking about the goal in terms of place value and estimation might have made this lesson aligned with common core.

#3 The Highlight for Me?

The highlight for me was at the end of the lesson, where we returned to the candy store. I offered the idea that I didn’t know which one would be bigger, but I knew they would be close, because 100*24 and 60*40 are both 2400. Another student offered the idea that if you ignore the “ones” place, then 5*4 = “20” and “9*2” = 18. That’s such a great idea. Not only is it insightful, but it explicitly built off learning that occurred during the lesson. The teacher said that our two ideas were the same, but I said I didn’t think so. I tried to revoice the students’ idea, and asked if that’s what she was saying. I think now I was estimating by rounding and multiplying, and the other student was estimating by attending to place value, but it didn’t occur to me at the time to say it that way. Our ideas are not entirely different for sure, because they both involve doing something to ignore the ones place.

Anyway, I think the lesson could probably be improved by having more of that–students’ sharing ideas, and a teacher facilitating sense making around those ideas. Of course, understanding and capitalizing on those ideas involves a lot of pedagogical content knowledge. But that student’s ideas could have gotten a lot of airtime, because it was like the perfect contribution.